General Factorization of the n -Point Beta Function into Two Parts in a Möbius-Invariant Manner
Joel A. Shapiro · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · 1970
Using the Koba-Nielsen formalism for the generalized beta function, a general form for factorization into two pieces is developed in an entirely M\"obius-invariant way. Ward identities for the vertex in the general configuration are derived in a manner which uses only the M\"obius invariance of that factor. Special cases (still M\"obius-invariant) of this procedure include the multiperipheral, semimultiperipheral, and symmetric factorizations already known.